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One of the ideas that died with Mitt Romney’s bid for the presidency was to create a federal school-voucher scheme.

The proposal would not have created full tuition vouchers — after all, most schools are funded directly from state coffers — but would have allowed small amounts of federal funding for special-needs and poor students to stay with the child, as opposed to going directly to schools.

Republicans and Democrats have found much common ground on education reform, with both parties taking a student-centred approach.

America is a rabidly individualistic country, so it is not surprising that the general thrust of reform has focused on increasing school choice, whether through charter schools (which have public funding and oversight) or allowing children to enroll in schools outside their traditional boundaries.

But with vouchers there is still plenty of disagreement. Republicans tend to want lots more of them, while most Democrats want nothing to do with them. Republicans chalk this up to pressure from the teachers unions.

Experience in Indiana shows that public schools have to raise their game, and compete with each other, to win students under voucher programmes. Even then students may decide to take their vouchers into the private sector. That is what concerns Barack Obama’s team, who don't want to see public schools, attended by the vast majority of children, drained of funds.

Earlier this year Mr Obama initially declined to expand the voucher programme in Washington, DC, putting him at odds with congressional Republicans. The programme has so far shown mixed results (voucher students have higher graduation rates, but get similar test scores compared to non-voucher students). In the end, the administration agreed to a small expansion of the programme, from 1,615 to 1,700 students.

According to the Washington Post, hundreds of these students are using their vouchers to attend schools that are unaccredited or in unconventional settings, where the government has no say over curriculum, quality or management.

The Post singles out "a family-run K-12 school operating out of a storefront, a Nation of Islam school based in a converted Deanwood residence, and a school built around the philosophy of a Bulgarian psychotherapist." This leads Matthew Yglesias of Slate to make an important and overlooked point: the idea that market competition alone will produce high-quality learning is fallacious. One need only look at the market for snack food, which is rather tasty but not very healthy, to see this.

Public schools are set up to educate children first and foremost, but also to ensure that they learn things deemed useful to society, rather than, say, yoga or skywriting. Certainly it is the right of parents to educate their children about things like yoga and skywriting (or how to practice Christianity or Islam), but they do not have the right to demand that society pay for it.

It may be unfashionable to say so, but the public does have a right to make sure that children schooled on public money learn things that we all consider useful. After all, these children will eventually be the doctors, scientists and engineers that fuel the economy and pay our retirement costs. This is not to say that vouchers can't be useful. But without some controls on where the vouchers are going, they may create more problems than they solve.